You have just started a coffee stand at the Saturday Market, and you prepare fresh brewed coffee every Saturday. Based on your analysis of the current market, you concluded that the demand for brewed coffee follows a normal distribution with the mean being 10 gallons and the standard deviation being 1.2 gallons. a. What is the probability that the demand for brewed coffee will be between 7 gallons and 13 gallons? b. In case you want to satisfy the demand 97% of time, how many gallons of brewed coffee do you need to prepare every Saturday? c. What is the range of the demand for brewed coffee with 97% certainty (i.e. 97% confidence interval of the demand)?
You have just started a coffee stand at the Saturday Market, and you prepare fresh brewed coffee every Saturday. Based on your analysis of the current market, you concluded that the demand for brewed coffee follows a normal distribution with the mean being 10 gallons and the standard deviation being 1.2 gallons. a. What is the probability that the demand for brewed coffee will be between 7 gallons and 13 gallons? b. In case you want to satisfy the demand 97% of time, how many gallons of brewed coffee do you need to prepare every Saturday? c. What is the range of the demand for brewed coffee with 97% certainty (i.e. 97% confidence interval of the demand)?
You have just started a coffee stand at the Saturday Market, and you prepare fresh brewed coffee every Saturday. Based on your analysis of the current market, you concluded that the demand for brewed coffee follows a normal distribution with the mean being 10 gallons and the standard deviation being 1.2 gallons. a. What is the probability that the demand for brewed coffee will be between 7 gallons and 13 gallons? b. In case you want to satisfy the demand 97% of time, how many gallons of brewed coffee do you need to prepare every Saturday? c. What is the range of the demand for brewed coffee with 97% certainty (i.e. 97% confidence interval of the demand)?
Transcribed Image Text:**Demand for Brewed Coffee at the Saturday Market**
You have just started a coffee stand at the Saturday Market, and you prepare fresh brewed coffee every Saturday. Based on your analysis of the current market, you concluded that the demand for brewed coffee follows a normal distribution with the mean being 10 gallons and the standard deviation being 1.2 gallons.
a. **What is the probability that the demand for brewed coffee will be between 7 gallons and 13 gallons?**
b. **In case you want to satisfy the demand 97% of the time, how many gallons of brewed coffee do you need to prepare every Saturday?**
c. **What is the range of the demand for brewed coffee with 97% certainty (i.e. 97% confidence interval of the demand)?**
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
